The EOQ and the savings in total inventory costs
Provide your detailed answers below every part of each question.
Avery owns four large dealerships in the metropolitan area. Each of these locations currently keep inventory of required components used for the repairs of the cars. It is possible for the company to keep all the high-priced parts at one of these locations and then deliver to any other location within one hour. The cost of space and the delivery vehicle is negligible but the labor cost of the driver for making all the required deliveries to all three locations will be $180 per day. You have been hired as a supply chain consultant to help Avery in making this decision. Use the following data to calculate the total relevant costs of both the current and the proposed scenario:
Average Price of the High-Priced Components = $150
Annual Demand for the High -Priced Components = 20,000 items per location
Number of Work-Days = 250 per year
Annual Holding Costs = 30% per year
Lead Time for replenishment from the manufacturer = 9 days
Fixed Costs of placing an order with the manufacturer = $150 per order
Target cycle service level = 0.95
a) Calculate the EOQ and the savings in total inventory costs for the current and the proposed scenario.
b) Now assume that the demand at each location is not constant but it is Normal with mean 100 and standard deviation of 15 High-Priced items per day. Calculate the cost of safety inventory for the current and the proposed scenario.
c) What is your recommendation and how much will Avery save if the demand was probabilistic?
a) Calculate the EOQ and the savings in total inventory costs for the current and the proposed scenario.
To calculate the Economic Order Quantity (EOQ), we can use the following formula:
EOQ = √((2DS) / H)
Where:
D = Annual demand
S = Ordering cost per order
H = Holding cost per unit per year
Given data:
Annual demand (D) = 20,000 items per location
Ordering cost (S) = $150 per order
Holding cost (H) = 30% per year
Calculating EOQ for the current scenario:
EOQ_current = √((2 * 20,000 * $150) / 0.3)
EOQ_current = √(6,000,000 / 0.3)
EOQ_current = √20,000,000
EOQ_current ≈ 4,472 items
Calculating EOQ for the proposed scenario:
EOQ_proposed = √((2 * 80,000 * $150) / 0.3)
EOQ_proposed = √(24,000,000 / 0.3)
EOQ_proposed = √80,000,000
EOQ_proposed ≈ 8,944 items
To calculate the savings in total inventory costs for the current and proposed scenarios, we need to consider both carrying costs and ordering costs.
Carrying costs for the current scenario:
Carrying costs_current = (EOQ_current / 2) * H * Average Price
Carrying costs_current = (4,472 / 2) * 0.3 * $150
Carrying costs_current ≈ $15,930
Ordering costs for the current scenario:
Ordering costs_current = (Annual demand / EOQ_current) * S
Ordering costs_current = (20,000 / 4,472) * $150
Ordering costs_current ≈ $668
Total inventory costs for the current scenario:
Total costs_current = Carrying costs_current + Ordering costs_current
Total costs_current ≈ $15,930 + $668
Total costs_current ≈ $16,598
Carrying costs for the proposed scenario:
Carrying costs_proposed = (EOQ_proposed / 2) * H * Average Price
Carrying costs_proposed = (8,944 / 2) * 0.3 * $150
Carrying costs_proposed ≈ $26,760
Ordering costs for the proposed scenario:
Ordering costs_proposed = (Annual demand / EOQ_proposed) * S
Ordering costs_proposed = (20,000 / 8,944) * $150
Ordering costs_proposed ≈ $335
Total inventory costs for the proposed scenario:
Total costs_proposed = Carrying costs_proposed + Ordering costs_proposed
Total costs_proposed ≈ $26,760 + $335
Total costs_proposed ≈ $27,095
Savings in total inventory costs:
Savings = Total costs_current - Total costs_proposed
Savings ≈ $16,598 - $27,095
Savings ≈ -$10,497
Therefore, there would be a cost increase of approximately $10,497 if Avery were to implement the proposed scenario.
b) Now assume that the demand at each location is not constant but it is Normal with mean 100 and standard deviation of 15 High-Priced items per day. Calculate the cost of safety inventory for the current and the proposed scenario.
To calculate the cost of safety inventory, we need to determine the safety stock level. The safety stock level is calculated using the following formula:
Safety Stock Level = Z * √(Lead Time * Variance of daily demand)
Where:
Z = Z-score representing desired service level
Lead Time = Lead time for replenishment from the manufacturer
Variance of daily demand = (Standard deviation of daily demand)^2
Given data:
Z-score (for a service level of 0.95) = 1.645
Lead Time = 9 days
Mean of daily demand = 100 items
Standard deviation of daily demand = 15 items
Calculating safety stock level for the current scenario:
Safety Stock Level_current = 1.645 * √(9 * (15^2))
Safety Stock Level_current ≈ 1.645 * √(9 * 225)
Safety Stock Level_current ≈ 1.645 * √2025
Safety Stock Level_current ≈ 1.645 * 45
Safety Stock Level_current ≈ 73.525
Calculating safety stock level for the proposed scenario:
Safety Stock Level_proposed = 1.645 * √(9 * (15^2))
Safety Stock Level_proposed ≈ 1.645 * √(9 * 225)
Safety Stock Level_proposed ≈ 1.645 * √2025
Safety Stock Level_proposed ≈ 1.645 * 45
Safety Stock Level_proposed ≈ 73.525
To calculate the cost of safety inventory, we need to multiply the safety stock level by the average price of high-priced components.
Cost of safety inventory for both scenarios:
Cost of Safety Inventory = Safety Stock Level * Average Price
Cost of Safety Inventory_current = 73.525 * $150
Cost of Safety Inventory_current ≈ $11,028.75
Cost of Safety Inventory_proposed = 73.525 * $150
Cost of Safety Inventory_proposed ≈ $11,028.75
Therefore, the cost of safety inventory remains the same for both the current and proposed scenarios at approximately $11,028.75.
c) What is your recommendation and how much will Avery save if the demand was probabilistic?
Based on the calculations above, it can be concluded that implementing the proposed scenario would result in a cost increase rather than savings. The total inventory costs for the proposed scenario are higher than those for the current scenario.
If the demand was probabilistic, Avery would still not save any money as the cost of safety inventory remains the same for both scenarios.
Therefore, my recommendation would be for Avery to stick with the current scenario where each location keeps inventory of required components. This would avoid additional labor costs associated with delivering parts between locations and also prevent an increase in total inventory costs.